Abstract :
Let Pn be an arbitrary regular polygon with n sides. What is the maximum number k(Pn) of congruent regular polygons (copies of Pn) that can be arranged so that each touches Pn but no two of them overlap? Youngs (1939), Klamkin (1995) and others established that k(P3) = 12, k(P4) = 8 and k(P6) = 6. In this paper, we will establish the general and nice result k(Pn) = 6. where n > 6.
